Can the DAMA annual modulation be explained by …...Can the DAMA annual modulation be explained by Dark Matter? Thomas Schwetz-Mangold MPIK, Heidelberg based on M. Fairbairn and T

Can the DAMA annual modulation be explained byDark Matter?

Thomas Schwetz-Mangold

MPIK, Heidelberg

based on M. Fairbairn and T. Schwetz, arXiv:0808.0704

T. Schwetz, MPIK, 24 Nov 2008 – p. 1

Outline

• Introduction• Review on DM direct detection phenomenology• recent DAMA/LIBRA results• DAMA vs XENON/CDMS for

spin-independent elastic DM scattering• Non-standard DM halos• Beyond SI elastic DM scattering• Summary


Introduction

R. Kolb, CERN academic training 2008 T. Schwetz, MPIK, 24 Nov 2008 – p. 3

Introduction


The CDM paradigm

a popular candidate for DM is a

Weakly Interacting Massive Particle


The CDM paradigm

a popular candidate for DM is a

Weakly Interacting Massive Particle

in the following I will try to be as model independentas possible:

I just assume that there is an unknown particlearound in our galaxy with some mass mχ andinteraction cross section σ, and consider thephenomenology for direct detection experiments

no constraints from collider searches will beconsidered


DM direct detection


DM direct detection

Look for recoil of DM-nucleus scattering:

χ + N → χ + N

cnts / kg-detector mass / keV recoil energy ER:

dN

dER

(t) =ρχ

mχ

σ(q)

2µ2χ

∫

v>vmin

d3vf⊕(~v, t)

v︸︷︷︸

≡η(ER,t)

ρχ DM energy density, default: 0.3 GeV cm−3

q =√

2MER momentum transfer

µχ = mχM/(mχ + M) reduced DM/nucleus mass

η(ER, t) integral over DM velocity distribution in lab frameT. Schwetz, MPIK, 24 Nov 2008 – p. 7

Cross section

in general there is a spin-independent andspin-dependent contribution to the DM-nucleonscattering cross section:

σ(q) = σSI(q) + σSD(q)


Cross section

spin-independent:

σSI(q) = σ0 |F (q)|2 , F (q) : nuclear form factor, (norm.: F (0) = 1)

σ0 =2µ2

χ

π[Zfp + (A − Z)fn]2 ≈ σp

µ2χ

µ2p

A2 for fp ≈ fn

spin-dependent:

σSD =32µ2

χG2F

2J + 1

[a2

pSpp(q) + apanSpn(q) + a2nSnn(q)

]

ap, an: couplings to proton and neutron

Spp(q), Spn(q), Snn(q): nuclear structure functions


Cross section

spin-independent:


σ0 =2µ2

χ


µ2χ

µ2p

A2 for fp ≈ fn

spin-dependent:

σSD =32µ2

χG2F

2J + 1

[a2


]



A2-enhancement of SI cross sectionT. Schwetz, MPIK, 24 Nov 2008 – p. 9

Cross section

spin-independent:


σ0 =2µ2

χ


µ2χ

µ2p

A2 for fp ≈ fn

consider first only SI contribution:

⇒ dN

dER

(t) =ρχ

mχ

σp|F (q)|2A2

2µ2p

η(ER, t)


Velocity distribution

η(ER, t) =

∫

v>vmin(ER)

d3vf⊕(~v, t)

v

v = |~v| : DM velocity in detector rest framevmin : minimal DM velocity required to produce recoil energy ER

vmin =

√

MER

2µ2χ

=mχ + M

mχ

√

ER

2M



η(ER, t) =

∫

v>vmin(ER)

d3vf⊕(~v, t)

v

v = |~v| : DM velocity in detector rest framevmin : minimal DM velocity required to produce recoil energy ER

vmin =

√

MER

2µ2χ

=mχ + M

mχ

√

ER

2M

obtain velocity distribution in Earth rest frame f⊕ fromdistribution in galaxy rest frame fgal:

f⊕(~v, t) = fgal(~v + ~v⊙ + ~v⊕(t))T. Schwetz, MPIK, 24 Nov 2008 – p. 11


f⊕(~v, t) = fgal(~v + ~v⊙ + ~v⊕(t))

“standard halo model”: Maxwellian velocity distribution

fgal(~v) =

N [exp (−v2/v2) − exp (−v2esc/v

2)] v < vesc

0 v > vesc

with v = 220 km/s and vesc = 650 km/s



f⊕(~v, t) = fgal(~v + ~v⊙ + ~v⊕(t))

sun velocity: ~v⊙ = (0, 220, 0) + (10, 13, 7) km/searth velocity: ~v⊕(t) with v⊕ ≈ 30 km/s


Velocity distribution integral

-600 -400 -200 0 200 400 600 800 1000v

y [km/s]

-600

-400

-200

0

200

400

600

800

1000

v z[k

m/s

]

center of galaxy: x-axis

vmin

for M = 118 GeV(127

I), m = 10 GeV

E R = 10 keV

5 keV3 keV

∫

v>vmin

d3vf⊕(~v, t)

v

vmin =

√

MER

2µ2χ



-600 -400 -200 0 200 400 600 800 1000v

y [km/s]

-600

-400

-200

0

200

400

600

800

1000

v z[k

m/s

]

center of galaxy: x-axis

vmin

for M = 118 GeV(127

I), m = 10 GeV, Erec

= 3 keV

June 2nd

Dec 2nd

∫

v>vmin

d3vf⊕(~v, t)

v



η(ER, t) ∝ 1

vobs(t)

∫ ∞

vmin(ER)

dv

[

e−

“

v−vobs(t)

v

”2

− e−

“

v+vobs(t)

v

”2]

0 200 400 600 800v [km/s]

velo

city

dis

trib

utio

n [a

rb. u

nits

]

0 200 400 600 8001

10

100

DM

mas

s [G

eV]

vmin

June 2nd

Dec. 2nd

M = 21.4 GeV (Na), Erec = 3 keV

M = 67.5 GeV (Ge), Erec = 10 keVM = 118 GeV (I), E

rec = 3 keV

vm

ean

vmin =

s

MER

2µ2χ

vobs(t) = |~v⊙ + ~v⊕(t)|


DAMA/LIBRA results


The DAMA experiment

search for a scinitillation signal in NaI crystals

DAMA/NaI ∼ 87.3 kg 7 yr 0.29 t yrDAMA/LIBRA ∼ 232.8 kg 4 yr 0.53 t yrtotal exposure: 0.82 t yr

DAMA/LIBRA consists of 25 detectors,9.70 kg each 10.2 × 10.2 × 25.4 cm2


The DAMA experiment

search for a scinitillation signal in NaI crystals

DAMA/NaI ∼ 87.3 kg 7 yr 0.29 t yrDAMA/LIBRA ∼ 232.8 kg 4 yr 0.53 t yrtotal exposure: 0.82 t yr

total single-hit scintillation signal in DAMA/LIBRA:

0

2

4

6

8

10

2 4 6 8 10 Energy (keV)

Rat

e (c

pd/k

g/ke

V)

∼ 1 cnts/d/kg/keV → ∼ 2 × 105 events/keV in DAMA/LIBRAT. Schwetz, MPIK, 24 Nov 2008 – p. 16

The DAMA annual modulation signal

evidence for an annual modulation of the count rate:Bernabei et al., 0804.2741

2-6 keV

Time (day)

Res

idua

ls (

cpd/

kg/k

eV) DAMA/NaI (0.29 ton×yr)

(target mass = 87.3 kg)DAMA/LIBRA (0.53 ton×yr)

(target mass = 232.8 kg)



fitting count rate with S0 + A cos ω(t − t0):

expectation for DM: T = 1 yr, t0 = 152 (2nd June)



fitting count rate with S0 + A cos ω(t − t0):

expectation for DM: T = 1 yr, t0 = 152 (2nd June)

8.2σ evidence for annual modulationT. Schwetz, MPIK, 24 Nov 2008 – p. 18

Energy dependence of the modulation signal

Energy (keV)

S m (

cpd/

kg/k

eV)

-0.05

-0.025

0

0.025

0.05

0 2 4 6 8 10 12 14 16 18 20

Sm (cpd/kg/keV)

Zm

(cp

d/kg

/keV

)

2-6 keV

6-14 keV

2σ contours

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

-0.03 -0.02 -0.01 0 0.01 0.02 0.03

modulation signal at 2 − 6 keVabove 6 keV no modulation

fitting:

S0 + Sm cos ω(t − t0) + Zm sin ω(t − t0)

with t0 = 152, T = 1 yr


Can this be explained by DM?


Can this be explained by DM?

• Yes, the DAMA signal can be explained,• but it is difficult to reconcile it with constraints from

other experiments.


Nuclear recoil signals

Rafael Lang @ Moriond EW 2008T. Schwetz, MPIK, 24 Nov 2008 – p. 21

Quenching

DAMA measures energy in“electron equivalent” (keVee)

only a fraction q of nuclear recoil energy ER isobservable as scintillation signal in DAMA:

Eobs = q × ER

with qNa = 0.3, qI = 0.09

⇒ the energy threshold of 2 keVee implies athreshold in ER of 6.7 keV for Na and 22 keV for I.


Channeling

Drobyshevski, 0706.3095; Bernabei et al., 0710.0288

with a certain probability a recoiling nucleus will not interact withthe crystal but loose its energy only electro-magnetically

for such “channeled” events q ≈ 1T. Schwetz, MPIK, 24 Nov 2008 – p. 23

Channeling

fraction of nuclear recoil events with q ≈ 1

ER (keV)

frac

tion

Iodine recoils

Sodium recoils

10-3

10-2

10-1

1

0 10 20 30 40 50 60

Bernabei et al., 0710.0288

channeling is important for low energy recoils


Channeling and DAMA

there are four types of events in the NaI of DAMA:

RDAMA(E) =

∑

x=Na,I

Mx

MNa + MI

{[1 − fx(E/qx)]Rx(E/qx)︸︷︷︸

quenched

+ fx(E)Rx(E)︸︷︷︸

channeled

}


Channeling and DAMA

there are four types of events in the NaI of DAMA:

★

★

★

★

1 10 100mχ [GeV]

10-42

10-41

10-40

10-39

10-38

σ p [cm

2 ]

1 10 100

Na quench

90%, 99.73% CL (2 dof)

I channel I quench

Na channel fitting DAMA requires

vmin =mχ + M

mχ

√

ER

2M

≈ 400 km/s

⇒


Fitting DAMA

★

1 10 100mχ [GeV]

10-42

10-41

10-40

10-39

σ p [cm

2 ]

1 10 100

best fit: mχ = 12 GeV

χ2

min = 36.8 / 34 dof

local minimum: mχ = 51 GeV

χ2

min = 47.9 / 34 dof (∆χ2

= 11.1)

90%, 99.73% CL (2 dof)


Fitting DAMA

★

1 10 100mχ [GeV]

10-42

10-41

10-40

10-39

σ p [cm

2 ]

1 10 100


χ2

min = 36.8 / 34 dof


χ2

min = 47.9 / 34 dof (∆χ2

= 11.1)

90%, 99.73% CL (2 dof)

energy shape of the mod-ulation is importantChang, Pierce, Weiner, 0808.0196Fairbairn, TS, 0808.0704

not included e.g., inGondolo, Gelmini, hep-ph/0504010Petriello, Zurek, 0806.3989

(only two bins: 2-6 keV and 6-14 keV)


Energy spectrum of the modulation

0 4 8 12 16 20E [keVee]

-0.01

0

0.01

0.02

0.03

0.04

coun

ts /

kg /

day

/ keV

ee

12 GeV, 1.3e-41 cm2

51 GeV, 7.8e-42 cm2

6 GeV, 2.8e-41 cm2

⇒T. Schwetz, MPIK, 24 Nov 2008 – p. 28

Fitting DAMA

★

1 10 100mχ [GeV]

10-42

10-41

10-40

10-39

σ p [cm

2 ]

1 10 100


χ2

min = 36.8 / 34 dof


χ2

min = 47.9 / 34 dof (∆χ2

= 11.1)

90%, 99.73% CL (2 dof)

prediction for total ratemust not exceed the ob-served number of eventsChang, Pierce, Weiner, 0808.0196Fairbairn, TS, 0808.0704


Prediction for total rate

2 3 4 5 6 7 8 9 10E [keVee]

0

0.5

1

1.5

coun

ts /

kg /

day

/ keV

ee

12 GeV, 1.3e-41 cm2

51 GeV, 7.8e-42 cm2

R(ER) = B(ER) + RDM(ER;mχ, σp) + A(ER;mχ, σp) cos ω(t − t0)

in a given model RDM and A are not independentT. Schwetz, MPIK, 24 Nov 2008 – p. 30

Constraints from other experiments

• CDMS:

exposure threshold M

CDMS-Si (2005) 12 kg day 7 keV 26 GeV

CDMS-Ge (2008) 121.3 kg day 10 keV 67 GeV

both CDMS-Si and CDMS-Ge observe zero events

• XENON10:

7 bins from 4.6 to 26.9 keV, 316 kg day exposure

10 candidate events: (1, 0, 0, 0, 3, 2, 4)


DAMA vs CDMS/XENON

★

1 10 100mχ [GeV]

10-42

10-41

10-40

10-39

σ p [cm

2 ]

1 10 100

CD

MS-G

eX

EN

ON

90%, 99.73% CL (2 dof)

DAMA

CDMS-Si

CoGeNT

DAMA 90% CL regionexcluded by 90% CLXENON, CDMS bounds

DAMA and XENONregions touch each otherat 3σ (∆χ2 = 11.2)

χ2min,glob = 62.9/(45 − 2)

(P ≈ 2%)

PPG = 2 × 10−6


DAMA vs CDMS/XENON

★

★

1 10 100mχ [GeV]

10-42

10-41

10-40

10-39

σ p [cm

2 ]

1 10 100

CD

MS-G

eX

EN

ON

90%, 99.73% CL (2 dof)

DAMA

CDMS-Si

CoGeNT

DAMAno channeling

DAMA 90% CL regionexcluded by 90% CLXENON, CDMS bounds

DAMA and XENONregions touch each otherat 3σ (∆χ2 = 11.2)

χ2min,glob = 62.9/(45 − 2)

(P ≈ 2%)

PPG = 2 × 10−6


Non-standard DM halos?


Via Lactea

N -body DM halo simulation (234 million particles)Diemand, Kuhlen, Madau, astro-ph/0611370


Via Lactea

N -body DM halo simulation (234 million particles)Diemand, Kuhlen, Madau, astro-ph/0611370

0 2 4 6 8 10r [ kpc ]

0.25

0.5

0.75

1

1.25

α

αR

αT

0 2 4 6 8 10r [ kpc ]

0

0.2

0.4

0.6

0.8

f

fR

fT

fitting radial and transvers distribution of Via Lactea data:

1

NRexp

[

−(

v2R

f 2R

)αR]

,2πvT

NTexp

[

−(

v2T

f 2T

)αT]


Via Lactea

★

10 100mχ [GeV]

10-42

10-41

10-40

σ p [cm

2 ]

10 100

CD

MS-G

eX

EN

ON

90%, 99.73% CL (2 dof)

DAMA

CDMS-Si

Via Lactea

(a)

χ2min,glob = 62.3/(45 − 2)

(P ≈ 2%)

PPG = 10−6


Non-standard Maxwellian halos

★

10 100mχ [GeV]

10-42

10-41

10-40

σ p [cm

2 ]

10 100

CD

MS-G

eX

EN

ON

90%, 99.73% CL (2 dof)

DAMA

CDMS-Si

Maxwellianv = 110 km/s

global

(b)

★

10 100mχ [GeV]

10-42

10-41

10-40

σ p [cm

2 ]

10 100

CD

MS-G

eX

EN

ON

90%, 99.73% CL (2 dof)

DAMA

CD

MS-Si

global

vR = 142 km/s

vT = 63 km/s

(c)

★

10 100mχ [GeV]

10-42

10-41

10-40

σ p [cm

2 ]

10 100

CD

MS-G

eX

EN

ON

90%, 99.73% CL (2 dof)

DAMA

CDMS-Si

vesc = 450 km/s

(d)


Non-standard Maxwellian halos

★

10 100mχ [GeV]

10-42

10-41

10-40

σ p [cm

2 ]

10 100

CD

MS-G

eX

EN

ON

90%, 99.73% CL (2 dof)

DAMA

CDMS-Si

Maxwellianv = 110 km/s

global

(b)

★

10 100mχ [GeV]

10-42

10-41

10-40

σ p [cm

2 ]

10 100

CD

MS-G

eX

EN

ON

90%, 99.73% CL (2 dof)

DAMA

CD

MS-Si

global

vR = 142 km/s

vT = 63 km/s

(c)

★

10 100mχ [GeV]

10-42

10-41

10-40

σ p [cm

2 ]

10 100

CD

MS-G

eX

EN

ON

90%, 99.73% CL (2 dof)

DAMA

CDMS-Si

vesc = 450 km/s

(d)

asymmetric halo with small vel. dispersion gives reasonable fitrather extreme assumptions on halo popertiesT. Schwetz, MPIK, 24 Nov 2008 – p. 35

DM streams

Gondolo, Gelmini, hep-ph/0504010; Chang, Pierce, Weiner, 0808.0196

vstr = 900 km/sσstr = 20 km/saligned with sun’s motion3% of halo DM density

marginal solutions appear atmχ ≈ 2 and 4 GeV


Beyond spin-independent elastic DM scattering

• spin-dependent scattering• inelastic scattering• DM scattering only on electrons


Spin-dependent scattering

in general there is a spin-independent and spin-dependentcontribution to the DM nucleon scattering cross section:

σ = σSI + σSD

with

σSD =32µ2

χG2F

2J + 1

[a2


]



remember: σSI ≈ σp(µχ/µp)2 A2 |F (q)|2 → A2-enhancement



coupling mainly to an un-paired nucleon:

neutron proton2311Na even odd12753 I even odd

12954 Xe, 131

54 Xe odd even7332Ge odd even

coupling with proton looks promising for DAMA



coupling mainly to an un-paired nucleon:

neutron proton2311Na even odd12753 I even odd

12954 Xe, 131

54 Xe odd even7332Ge odd even

coupling with proton looks promising for DAMA

BUT: strong constraint from Super-Kamiokande bound onneutrinos from DM annihilations in the sunSavage, Gelmini, Gondolo, Freese, 0808.3607Hooper, Petriello, Zurek, Kamionkowski, 0808.2464


SD scattering: neutron-only coupling

Savage, Gelmini, Gondolo, Freese, 0808.3607

100 101 102 10310-4

10-3

10-2

10-1

100

101

102

103

104

MWIMP HGeVL

ΣΧ

nHp

bL

spin-dependentHap = 0, neutron onlyL CDMS I Si

CDMS II Ge

XENON 10

CoGeNT

TEXONO

CRESST I

DAMA H3Σ�90%Lwith channeling

DAMA H7Σ�5ΣLwith channeling

DAMA H3Σ�90%L

DAMA H7Σ�5ΣL


SD scattering: proton-only coupling

Savage, Gelmini, Gondolo, Freese, 0808.3607

100 101 102 10310-4

10-3

10-2

10-1

100

101

102

103

104

MWIMP HGeVL

ΣΧ

pHp

bL

spin-dependentHan = 0, proton onlyL CDMS I Si

CDMS II Ge

XENON 10

Super-K

CoGeNT

TEXONO

CRESST I

DAMA H3Σ�90%Lwith channeling

DAMA H7Σ�5ΣLwith channeling

DAMA H3Σ�90%L

DAMA H7Σ�5ΣL

constraint from COUPP: σpSD . 1 pb @ mχ . 10 GeV


Inelastic DM scattering

Tucker-Smith, Weiner, hep-ph/0101138, hep-ph/0402065;Chang, Kribs, Tucker-Smith, Weiner, 0807.2250

• in addition to the DM χ there exists an excitedstate χ∗, with a mass splitting

mχ∗ − mχ = δ ≃ 100 keV ∼ 10−6mχ

• elastic scattering χ + N → χ + N is suppressedwith respect to inelastic scattering

χ + N → χ∗ + N



0 20 40 60 80 100E

R [keV]

0

200

400

600

800

1000

v min

[km

/s]

GeI, Xe

elastic

inelastic

mχ = 120 GeV, δ = 100 keV

vinelmin =

1√2MER

(MER

µχ

+ δ

)

velmin =

√

MER

2

1

µχ

• sampling only high-velocity tail of velocity distribution

• no events at low recoil energies

• targets with high mass are favouredT. Schwetz, MPIK, 24 Nov 2008 – p. 43


Chang, Kribs, Tucker-Smith, Weiner, 0807.2250

leads to very different event spectrum as in case ofelastic scattering (exponentially falling)





Chang, Kribs, Tucker-Smith, Weiner, 0807.2250

XENON, ZEPLIN, and CRESST have seen already DM!T. Schwetz, MPIK, 24 Nov 2008 – p. 46

DM scattering off electrons

DAMA observes just scitillation light, XENON andCDMS require the coincidence of two signals ⇒

If DM interacted only with electrons, it would not showup in XENON/CDMS but could provide the DAMAannual modulation.



To deposit & 2 keV by χ + e− → χ + e− the electron cannot be atrest ⇒ explore scattering on electrons bound to the nucleus.

mχo (GeV)

E+

(keV

)

p = 0.1 MeV/c

p = 1 MeV/c

p = 5 MeV/c

10-1

1

10

10-1

1 10 102

103

in NaI the e− have p & 0.5 MeVwith a probability ∼ 10−4

max. released energy forvχ = (0.001 − 0.002)c and θ = π




To deposit & 2 keV by χ + e− → χ + e− the electron cannot be atrest ⇒ explore scattering on electrons bound to the nucleus.

mχo (GeV)

ξσe0

(pb)

10-3

10-2

10-1

1

10

10 2

500 1000 1500 2000

in NaI the e− have p & 0.5 MeVwith a probability ∼ 10−4



Summary


Summary

• DAMA observes an annual modulation of theircount rate at a significance of 8.2σ.The phase is in agreement with DM scattering.


Summary


• An interpretation of this signal in terms of SIelastic DM scattering is in conflict with boundsfrom XENON and CDMS at the level of 3σ.


Summary


• An interpretation of this signal in terms of SIelastic DM scattering is in conflict with boundsfrom XENON and CDMS at the level of 3σ.

• Reconciling the data seems to require veryextreme assumptions on DM halo properties.


Summary

Beyond spin-independent scattering:

• Spin-dependent scattering on protons can evadethe bounds from XENON and CDMS, but thenstrong constraints from Super-Kamiokandeindirect DM searches apply.


Summary



• Inelastic DM scattering allows an explanation ofthe DAMA signal which is going to be tested soonby the CRESST experiment.


Summary



• Inelastic DM scattering allows an explanation ofthe DAMA signal which is going to be tested soonby the CRESST experiment.

• DM scattering off electrons seems to be aphenomenologically valid explanation.


Thank you for your attention!


Additional slides


Dropping the first energy bin

0 4 8 12 16 20E [keVee]

-0.01

0

0.01

0.02

0.03

0.04

coun

ts /

kg /

day

/ keV

ee

12 GeV, 1.3e-41 cm2

51 GeV, 7.8e-42 cm2

6 GeV, 2.8e-41 cm2

★

1 10mχ [GeV]

10-42

10-41

10-40

10-39

10-38

σ p [cm

2 ]1 10

CD

MS-G

eX

EN

ON

90%, 99.73% CL (2 dof)

DAMA

CDMS-Si

without 1st

bin

global

χ2DAMA,min mDAMA

χ,best χ2glob,min GOF χ2

PG PG mglobχ,best

default 36.8 12 62.9 0.02 26.1 2 × 10−6 8.6

w/o 1st bin 30.3 10 40.4 0.50 10.1 6 × 10−3 3.9


Exclusion curves depend on energy threshold

ex.: new evaluation of Leff in XENON:“scintillation yield of Xe for nuclear recoils, relative to thezero-field scintillation yield for electron recoils at 122 keVee.”

Sorensen et al., 0807.0459

ER =S1

LyLeff

Se

Sn

Leff ≈ 0.15 instead of 0.19

at low energies moves thethreshold of 4.6 keV toabout 6 keV


Exclusion curves depend on energy threshold

ex.: new evaluation of Leff in XENON:“scintillation yield of Xe for nuclear recoils, relative to thezero-field scintillation yield for electron recoils at 122 keVee.”

E. Aprile @ idm2008, Stockholm

ER =S1

LyLeff

Se

Sn

Leff ≈ 0.15 instead of 0.19

at low energies moves thethreshold of 4.6 keV toabout 6 keV


Documents

Can the DAMA annual modulation be explained by …...Can the DAMA annual modulation be explained by Dark Matter? Thomas Schwetz-Mangold MPIK, Heidelberg based on M. Fairbairn and T